def __init__(self, parent, nkpt, displacement=None, size=None, trs=True):
super(MonkhorstPack, self).__init__(parent)
if isinstance(nkpt, Integral):
nkpt = np.diag([nkpt] * 3)
elif isinstance(nkpt[0], Integral):
nkpt = np.diag(nkpt)
# Now we have a matrix of k-points
if np.any(nkpt - np.diag(np.diag(nkpt)) != 0):
raise NotImplementedError(
self.__class__.__name__ +
" with off-diagonal components is not implemented yet")
if displacement is None:
displacement = np.zeros(3, np.float64)
elif isinstance(displacement, Real):
displacement = np.zeros(3, np.float64) + displacement
if size is None:
size = _a.onesd(3)
elif isinstance(size, Real):
size = _a.zerosd(3) + size
# Retrieve the diagonal number of values
Dn = np.diag(nkpt).astype(np.int32)
if np.any(Dn) == 0:
raise ValueError(self.__class__.__name__ +
' *must* be initialized with '
'diagonal elements different from 0.')
i_trs = -1
if trs:
# Figure out which direction to TRS
nmax = 0
for i in [0, 1, 2]:
if displacement[i] == 0. and Dn[i] > nmax:
nmax = Dn[i]
i_trs = i
# Calculate k-points and weights along all directions
kw = [
self.grid(Dn[i], displacement[i], size[i], i == i_trs)
for i in (0, 1, 2)
]
self._k = _a.emptyd((kw[0][0].size, kw[1][0].size, kw[2][0].size, 3))
self._w = _a.onesd(self._k.shape[:-1])
for i in (0, 1, 2):
k = kw[i][0].reshape(-1, 1, 1)
w = kw[i][1].reshape(-1, 1, 1)
self._k[..., i] = np.rollaxis(k, 0, i + 1)
self._w[...] *= np.rollaxis(w, 0, i + 1)
del kw
self._k.shape = (-1, 3)
self._k = np.where(self._k > .5, self._k - 1, self._k)
self._w.shape = (-1, )
def grid(n, displ=0., size=1., trs=False):
r""" Create a grid of `n` points with an offset of `displ` and sampling `size` around `displ`
The :math:`k`-points are :math:`\Gamma` centered.
Parameters
----------
n : int
number of points in the grid. If `trs` is ``True`` this may be smaller than `n`
displ : float, optional
the displacement of the grid
size : float, optional
the total size of the Brillouin zone to sample
trs : bool, optional
whether time-reversal-symmetry is applied
Returns
-------
k : np.ndarray
the list of k-points in the Brillouin zone to be sampled
w : np.ndarray
weights for the k-points
"""
# First ensure that displ is in the Brillouin
displ = displ % 1.
if displ > 0.5:
displ -= 1.
if trs and displ == 0.:
n_half = n // 2
if n % 2 == 1:
# Odd case, we have Gamma and remove all negative values
k = _a.aranged(n_half + 1) * size / n + displ
# Weights are all twice (except Gamma)
w = _a.onesd(len(k)) / n * size
w[1:] *= 2
else:
# Even case, we do not have Gamma, but we shift to Gamma
# All points except Gamma and edge have weights doubled
k = _a.aranged(n_half + 1) * size / n + displ
# Weights are all twice (except Gamma and band-edge)
w = _a.onesd(len(k)) / n * size
w[1:-1] *= 2
else:
# Not TRS
if n % 2 == 0:
k = (_a.aranged(n) * 2 - n) * size / (2 * n) + displ
else:
k = (_a.aranged(n) * 2 - n + 1) * size / (2 * n) + displ
w = _a.onesd(n) * size / n
# Return values
return k, w
def _setup(self, *args, **kwargs):
""" Setup the special object for data containing """
self._data = dict()
if self._access > 0:
# Fake double calls
access = self._access
self._access = 0
# There are certain elements which should
# be minimal on memory but allow for
# fast access by the object.
for d in ['cell', 'xa', 'lasto', 'E']:
self._data[d] = self._value(d)
# tbtrans does not store the k-points and weights
# if the Gamma-point is used.
try:
self._data['kpt'] = self._value('kpt')
except:
self._data['kpt'] = _a.zerosd([3])
try:
self._data['wkpt'] = self._value('wkpt')
except:
self._data['wkpt'] = _a.onesd([1])
# Create the geometry in the data file
self._data['_geom'] = self.read_geometry()
# Reset the access pattern
self._access = access
def __init__(self, parent, k=None, weight=None):
self.set_parent(parent)
# Gamma point
if k is None:
self._k = _a.zerosd([1, 3])
self._w = _a.onesd(1)
else:
self._k = _a.arrayd(k).reshape(-1, 3)
if weight is None:
n = self._k.shape[0]
self._w = _a.onesd(n) / n
else:
self._w = _a.arrayd(weight).ravel()
if len(self.k) != len(self.weight):
raise ValueError(self.__class__.__name__ + '.__init__ requires input k-points and weights to be of equal length.')
# Instantiate the array call
self.asarray()
def __init__(self, parent):
try:
# It probably has the supercell attached
parent.cell
parent.rcell
self.parent = parent
except:
self.parent = SuperCell(parent)
# Gamma point
self._k = _a.zerosd([1, 3])
self._w = _a.onesd(1)
# Instantiate the array call
self.asarray()
def density(self, grid, spinor=None, tol=1e-7, eta=False):
r""" Expand the density matrix to the charge density on a grid
This routine calculates the real-space density components on a specified grid.
This is an *in-place* operation that *adds* to the current values in the grid.
Note: To calculate :math:`\rho(\mathbf r)` in a unit-cell different from the
originating geometry, simply pass a grid with a unit-cell different than the originating
supercell.
The real-space density is calculated as:
.. math::
\rho(\mathbf r) = \sum_{\nu\mu}\phi_\nu(\mathbf r)\phi_\mu(\mathbf r) D_{\nu\mu}
While for non-collinear/spin-orbit calculations the density is determined from the
spinor component (`spinor`) by
.. math::
\rho_{\boldsymbol\sigma}(\mathbf r) = \sum_{\nu\mu}\phi_\nu(\mathbf r)\phi_\mu(\mathbf r) \sum_\alpha [\boldsymbol\sigma \mathbf \rho_{\nu\mu}]_{\alpha\alpha}
Here :math:`\boldsymbol\sigma` corresponds to a spinor operator to extract relevant quantities. By passing the identity matrix the total charge is added. By using the Pauli matrix :math:`\boldsymbol\sigma_x`
only the :math:`x` component of the density is added to the grid (see `Spin.X`).
Parameters
----------
grid : Grid
the grid on which to add the density (the density is in ``e/Ang^3``)
spinor : (2,) or (2, 2), optional
the spinor matrix to obtain the diagonal components of the density. For un-polarized density matrices
this keyword has no influence. For spin-polarized it *has* to be either 1 integer or a vector of
length 2 (defaults to total density).
For non-collinear/spin-orbit density matrices it has to be a 2x2 matrix (defaults to total density).
tol : float, optional
DM tolerance for accepted values. For all density matrix elements with absolute values below
the tolerance, they will be treated as strictly zeros.
eta: bool, optional
show a progressbar on stdout
"""
try:
# Once unique has the axis keyword, we know we can safely
# use it in this routine
# Otherwise we raise an ImportError
unique([[0, 1], [2, 3]], axis=0)
except:
raise NotImplementedError(
self.__class__.__name__ +
'.density requires numpy >= 1.13, either update '
'numpy or do not use this function!')
geometry = self.geometry
# Check that the atomic coordinates, really are all within the intrinsic supercell.
# If not, it may mean that the DM does not conform to the primary unit-cell paradigm
# of matrix elements. It complicates things.
fxyz = geometry.fxyz
f_min = fxyz.min()
f_max = fxyz.max()
if f_min < 0 or 1. < f_max:
warn(
self.__class__.__name__ +
'.density has been passed a geometry where some coordinates are '
'outside the primary unit-cell. This may potentially lead to problems! '
'Double check the charge density!')
del fxyz, f_min, f_max
# Extract sub variables used throughout the loop
shape = _a.asarrayi(grid.shape)
dcell = grid.dcell
# Sparse matrix data
csr = self._csr
# In the following we don't care about division
# So 1) save error state, 2) turn off divide by 0, 3) calculate, 4) turn on old error state
old_err = np.seterr(divide='ignore', invalid='ignore')
# Placeholder for the resulting coefficients
DM = None
if self.spin.kind > Spin.POLARIZED:
if spinor is None:
# Default to the total density
spinor = np.identity(2, dtype=np.complex128)
else:
spinor = _a.arrayz(spinor)
if spinor.size != 4 or spinor.ndim != 2:
raise ValueError(
self.__class__.__name__ +
'.density with NC/SO spin, requires a 2x2 matrix.')
DM = _a.emptyz([self.nnz, 2, 2])
idx = array_arange(csr.ptr[:-1], n=csr.ncol)
if self.spin.kind == Spin.NONCOLINEAR:
# non-collinear
DM[:, 0, 0] = csr._D[idx, 0]
DM[:, 1, 1] = csr._D[idx, 1]
DM[:, 1,
0] = csr._D[idx,
2] - 1j * csr._D[idx, 3] #TODO check sign here!
DM[:, 0, 1] = np.conj(DM[:, 1, 0])
else:
# spin-orbit
DM[:, 0, 0] = csr._D[idx, 0] + 1j * csr._D[idx, 4]
DM[:, 1, 1] = csr._D[idx, 1] + 1j * csr._D[idx, 5]
DM[:, 1,
0] = csr._D[idx,
2] - 1j * csr._D[idx, 3] #TODO check sign here!
DM[:, 0, 1] = csr._D[idx, 6] + 1j * csr._D[idx, 7]
# Perform dot-product with spinor, and take out the diagonal real part
DM = dot(DM, spinor.T)[:, [0, 1], [0, 1]].sum(1).real
elif self.spin.kind == Spin.POLARIZED:
if spinor is None:
spinor = _a.onesd(2)
elif isinstance(spinor, Integral):
# extract the provided spin-polarization
s = _a.zerosd(2)
s[spinor] = 1.
spinor = s
else:
spinor = _a.arrayd(spinor)
if spinor.size != 2 or spinor.ndim != 1:
raise ValueError(
self.__class__.__name__ +
'.density with polarized spin, requires spinor '
'argument as an integer, or a vector of length 2')
idx = array_arange(csr.ptr[:-1], n=csr.ncol)
DM = csr._D[idx, 0] * spinor[0] + csr._D[idx, 1] * spinor[1]
else:
idx = array_arange(csr.ptr[:-1], n=csr.ncol)
DM = csr._D[idx, 0]
# Create the DM csr matrix.
csrDM = csr_matrix(
(DM, csr.col[idx], np.insert(np.cumsum(csr.ncol), 0, 0)),
shape=(self.shape[:2]),
dtype=DM.dtype)
# Clean-up
del idx, DM
# To heavily speed up the construction of the density we can recreate
# the sparse csrDM matrix by summing the lower and upper triangular part.
# This means we only traverse the sparse UPPER part of the DM matrix
# I.e.:
# psi_i * DM_{ij} * psi_j + psi_j * DM_{ji} * psi_i
# is equal to:
# psi_i * (DM_{ij} + DM_{ji}) * psi_j
# Secondly, to ease the loops we extract the main diagonal (on-site terms)
# and store this for separate usage
csr_sum = [None] * geometry.n_s
no = geometry.no
primary_i_s = geometry.sc_index([0, 0, 0])
for i_s in range(geometry.n_s):
# Extract the csr matrix
o_start, o_end = i_s * no, (i_s + 1) * no
csr = csrDM[:, o_start:o_end]
if i_s == primary_i_s:
csr_sum[i_s] = triu(csr) + tril(csr, -1).transpose()
else:
csr_sum[i_s] = csr
# Recreate the column-stacked csr matrix
csrDM = ss_hstack(csr_sum, format='csr')
del csr, csr_sum
# Remove all zero elements (note we use the tolerance here!)
csrDM.data = np.where(np.fabs(csrDM.data) > tol, csrDM.data, 0.)
# Eliminate zeros and sort indices etc.
csrDM.eliminate_zeros()
csrDM.sort_indices()
csrDM.prune()
# 1. Ensure the grid has a geometry associated with it
sc = grid.sc.copy()
if grid.geometry is None:
# Create the actual geometry that encompass the grid
ia, xyz, _ = geometry.within_inf(sc)
if len(ia) > 0:
grid.set_geometry(Geometry(xyz, geometry.atom[ia], sc=sc))
# Instead of looping all atoms in the supercell we find the exact atoms
# and their supercell indices.
add_R = _a.zerosd(3) + geometry.maxR()
# Calculate the required additional vectors required to increase the fictitious
# supercell by add_R in each direction.
# For extremely skewed lattices this will be way too much, hence we make
# them square.
o = sc.toCuboid(True)
sc = SuperCell(o._v, origo=o.origo) + np.diag(2 * add_R)
sc.origo -= add_R
# Retrieve all atoms within the grid supercell
# (and the neighbours that connect into the cell)
IA, XYZ, ISC = geometry.within_inf(sc)
# Retrieve progressbar
eta = tqdm_eta(len(IA), self.__class__.__name__ + '.density', 'atom',
eta)
cell = geometry.cell
atom = geometry.atom
axyz = geometry.axyz
a2o = geometry.a2o
def xyz2spherical(xyz, offset):
""" Calculate the spherical coordinates from indices """
rx = xyz[:, 0] - offset[0]
ry = xyz[:, 1] - offset[1]
rz = xyz[:, 2] - offset[2]
# Calculate radius ** 2
xyz_to_spherical_cos_phi(rx, ry, rz)
return rx, ry, rz
def xyz2sphericalR(xyz, offset, R):
""" Calculate the spherical coordinates from indices """
rx = xyz[:, 0] - offset[0]
idx = indices_fabs_le(rx, R)
ry = xyz[idx, 1] - offset[1]
ix = indices_fabs_le(ry, R)
ry = ry[ix]
idx = idx[ix]
rz = xyz[idx, 2] - offset[2]
ix = indices_fabs_le(rz, R)
ry = ry[ix]
rz = rz[ix]
idx = idx[ix]
if len(idx) == 0:
return [], [], [], []
rx = rx[idx]
# Calculate radius ** 2
ix = indices_le(rx**2 + ry**2 + rz**2, R**2)
idx = idx[ix]
if len(idx) == 0:
return [], [], [], []
rx = rx[ix]
ry = ry[ix]
rz = rz[ix]
xyz_to_spherical_cos_phi(rx, ry, rz)
return idx, rx, ry, rz
# Looping atoms in the sparse pattern is better since we can pre-calculate
# the radial parts and then add them.
# First create a SparseOrbital matrix, then convert to SparseAtom
spO = SparseOrbital(geometry, dtype=np.int16)
spO._csr = SparseCSR(csrDM)
spA = spO.toSparseAtom(dtype=np.int16)
del spO
na = geometry.na
# Remove the diagonal part of the sparse atom matrix
off = na * primary_i_s
for ia in range(na):
del spA[ia, off + ia]
# Get pointers and delete the atomic sparse pattern
# The below complexity is because we are not finalizing spA
csr = spA._csr
a_ptr = np.insert(_a.cumsumi(csr.ncol), 0, 0)
a_col = csr.col[array_arange(csr.ptr, n=csr.ncol)]
del spA, csr
# Get offset in supercell in orbitals
off = geometry.no * primary_i_s
origo = grid.origo
# TODO sum the non-origo atoms to the csrDM matrix
# this would further decrease the loops required.
# Loop over all atoms in the grid-cell
for ia, ia_xyz, isc in zip(IA, XYZ - origo.reshape(1, 3), ISC):
# Get current atom
ia_atom = atom[ia]
IO = a2o(ia)
IO_range = range(ia_atom.no)
cell_offset = (cell * isc.reshape(3, 1)).sum(0) - origo
# Extract maximum R
R = ia_atom.maxR()
if R <= 0.:
warn("Atom '{}' does not have a wave-function, skipping atom.".
format(ia_atom))
eta.update()
continue
# Retrieve indices of the grid for the atomic shape
idx = grid.index(ia_atom.toSphere(ia_xyz))
# Now we have the indices for the largest orbital on the atom
# Subsequently we have to loop the orbitals and the
# connecting orbitals
# Then we find the indices that overlap with these indices
# First reduce indices to inside the grid-cell
idx[idx[:, 0] < 0, 0] = 0
idx[shape[0] <= idx[:, 0], 0] = shape[0] - 1
idx[idx[:, 1] < 0, 1] = 0
idx[shape[1] <= idx[:, 1], 1] = shape[1] - 1
idx[idx[:, 2] < 0, 2] = 0
idx[shape[2] <= idx[:, 2], 2] = shape[2] - 1
# Remove duplicates, requires numpy >= 1.13
idx = unique(idx, axis=0)
if len(idx) == 0:
eta.update()
continue
# Get real-space coordinates for the current atom
# as well as the radial parts
grid_xyz = dot(idx, dcell)
# Perform loop on connection atoms
# Allocate the DM_pj arrays
# This will have a size equal to number of elements times number of
# orbitals on this atom
# In this way we do not have to calculate the psi_j multiple times
DM_io = csrDM[IO:IO + ia_atom.no, :].tolil()
DM_pj = _a.zerosd([ia_atom.no, grid_xyz.shape[0]])
# Now we perform the loop on the connections for this atom
# Remark that we have removed the diagonal atom (it-self)
# As that will be calculated in the end
for ja in a_col[a_ptr[ia]:a_ptr[ia + 1]]:
# Retrieve atom (which contains the orbitals)
ja_atom = atom[ja % na]
JO = a2o(ja)
jR = ja_atom.maxR()
# Get actual coordinate of the atom
ja_xyz = axyz(ja) + cell_offset
# Reduce the ia'th grid points to those that connects to the ja'th atom
ja_idx, ja_r, ja_theta, ja_cos_phi = xyz2sphericalR(
grid_xyz, ja_xyz, jR)
if len(ja_idx) == 0:
# Quick step
continue
# Loop on orbitals on this atom
for jo in range(ja_atom.no):
o = ja_atom.orbital[jo]
oR = o.R
# Downsize to the correct indices
if jR - oR < 1e-6:
ja_idx1 = ja_idx.view()
ja_r1 = ja_r.view()
ja_theta1 = ja_theta.view()
ja_cos_phi1 = ja_cos_phi.view()
else:
ja_idx1 = indices_le(ja_r, oR)
if len(ja_idx1) == 0:
# Quick step
continue
# Reduce arrays
ja_r1 = ja_r[ja_idx1]
ja_theta1 = ja_theta[ja_idx1]
ja_cos_phi1 = ja_cos_phi[ja_idx1]
ja_idx1 = ja_idx[ja_idx1]
# Calculate the psi_j component
psi = o.psi_spher(ja_r1,
ja_theta1,
ja_cos_phi1,
cos_phi=True)
# Now add this orbital to all components
for io in IO_range:
DM_pj[io, ja_idx1] += DM_io[io, JO + jo] * psi
# Temporary clean up
del ja_idx, ja_r, ja_theta, ja_cos_phi
del ja_idx1, ja_r1, ja_theta1, ja_cos_phi1, psi
# Now we have all components for all orbitals connection to all orbitals on atom
# ia. We simply need to add the diagonal components
# Loop on the orbitals on this atom
ia_r, ia_theta, ia_cos_phi = xyz2spherical(grid_xyz, ia_xyz)
del grid_xyz
for io in IO_range:
# Only loop halve the range.
# This is because: triu + tril(-1).transpose()
# removes the lower half of the on-site matrix.
for jo in range(io + 1, ia_atom.no):
DM = DM_io[io, off + IO + jo]
oj = ia_atom.orbital[jo]
ojR = oj.R
# Downsize to the correct indices
if R - ojR < 1e-6:
ja_idx1 = slice(None)
ja_r1 = ia_r.view()
ja_theta1 = ia_theta.view()
ja_cos_phi1 = ia_cos_phi.view()
else:
ja_idx1 = indices_le(ia_r, ojR)
if len(ja_idx1) == 0:
# Quick step
continue
# Reduce arrays
ja_r1 = ia_r[ja_idx1]
ja_theta1 = ia_theta[ja_idx1]
ja_cos_phi1 = ia_cos_phi[ja_idx1]
# Calculate the psi_j component
DM_pj[io, ja_idx1] += DM * oj.psi_spher(
ja_r1, ja_theta1, ja_cos_phi1, cos_phi=True)
# Calculate the psi_i component
# Note that this one *also* zeroes points outside the shell
# I.e. this step is important because it "nullifies" all but points where
# orbital io is defined.
psi = ia_atom.orbital[io].psi_spher(ia_r,
ia_theta,
ia_cos_phi,
cos_phi=True)
DM_pj[io, :] += DM_io[io, off + IO + io] * psi
DM_pj[io, :] *= psi
# Temporary clean up
ja_idx1 = ja_r1 = ja_theta1 = ja_cos_phi1 = None
del ia_r, ia_theta, ia_cos_phi, psi, DM_io
# Now add the density
grid.grid[idx[:, 0], idx[:, 1], idx[:, 2]] += DM_pj.sum(0)
# Clean-up
del DM_pj, idx
eta.update()
eta.close()
# Reset the error code for division
np.seterr(**old_err)
def __init__(self, parent, nkpt, displacement=None, size=None, centered=True, trs=True):
super(MonkhorstPack, self).__init__(parent)
if isinstance(nkpt, Integral):
nkpt = np.diag([nkpt] * 3)
elif isinstance(nkpt[0], Integral):
nkpt = np.diag(nkpt)
# Now we have a matrix of k-points
if np.any(nkpt - np.diag(np.diag(nkpt)) != 0):
raise NotImplementedError(self.__class__.__name__ + " with off-diagonal components is not implemented yet")
if displacement is None:
displacement = np.zeros(3, np.float64)
elif isinstance(displacement, Real):
displacement = np.zeros(3, np.float64) + displacement
if size is None:
size = _a.onesd(3)
elif isinstance(size, Real):
size = _a.zerosd(3) + size
else:
size = _a.arrayd(size)
# Retrieve the diagonal number of values
Dn = np.diag(nkpt).astype(np.int32)
if np.any(Dn) == 0:
raise ValueError(self.__class__.__name__ + ' *must* be initialized with '
'diagonal elements different from 0.')
i_trs = -1
if trs:
# Figure out which direction to TRS
nmax = 0
for i in [0, 1, 2]:
if displacement[i] in [0., 0.5] and Dn[i] > nmax:
nmax = Dn[i]
i_trs = i
if nmax == 1:
i_trs = -1
if i_trs == -1:
# If we still haven't decided (say for weird displacements)
# simply take the one with the maximum number of k-points.
i_trs = np.argmax(Dn)
# Calculate k-points and weights along all directions
kw = [self.grid(Dn[i], displacement[i], size[i], centered, i == i_trs) for i in (0, 1, 2)]
self._k = _a.emptyd((kw[0][0].size, kw[1][0].size, kw[2][0].size, 3))
self._w = _a.onesd(self._k.shape[:-1])
for i in (0, 1, 2):
k = kw[i][0].reshape(-1, 1, 1)
w = kw[i][1].reshape(-1, 1, 1)
self._k[..., i] = np.rollaxis(k, 0, i + 1)
self._w[...] *= np.rollaxis(w, 0, i + 1)
del kw
self._k.shape = (-1, 3)
self._k = np.where(self._k > .5, self._k - 1, self._k)
self._w.shape = (-1,)
# Store information regarding size and diagonal elements
# This information is basically only necessary when
# we want to replace special k-points
self._diag = Dn # vector
self._displ = displacement # vector
self._size = size # vector
self._centered = centered
self._trs = i_trs
def grid(cls, n, displ=0., size=1., centered=True, trs=False):
r""" Create a grid of `n` points with an offset of `displ` and sampling `size` around `displ`
The :math:`k`-points are :math:`\Gamma` centered.
Parameters
----------
n : int
number of points in the grid. If `trs` is ``True`` this may be smaller than `n`
displ : float, optional
the displacement of the grid
size : float, optional
the total size of the Brillouin zone to sample
centered : bool, optional
if the points are centered
trs : bool, optional
whether time-reversal-symmetry is applied
Returns
-------
k : np.ndarray
the list of k-points in the Brillouin zone to be sampled
w : np.ndarray
weights for the k-points
"""
# First ensure that displ is in the Brillouin
displ = displ % 1.
if displ > 0.5:
displ -= 1.
if displ < -0.5:
displ += 1.
# Centered _only_ has effect IFF
# displ == 0. and size == 1
# Otherwise we resort to other schemes
if displ != 0. or size != 1.:
centered = False
# We create the full grid, then afterwards we figure out TRS
n_half = n // 2
if n % 2 == 1:
k = _a.aranged(-n_half, n_half + 1) * size / n + displ
else:
k = _a.aranged(-n_half, n_half) * size / n + displ
if not centered:
# Shift everything by halve the size each occupies
k += size / (2 * n)
# Move k to the primitive cell and generate weights
k = cls.in_primitive(k)
w = _a.onesd(n) * size / n
# Check for TRS points
if trs and np.any(k < 0.):
# Make all positive to remove the double conting terms
k_pos = np.abs(k)
# Sort k-points and weights
idx = np.argsort(k_pos)
# Re-arange according to k value
k_pos = k_pos[idx]
w = w[idx]
# Find indices of all equivalent k-points (tolerance of 1e-10 in reciprocal units)
# 1e-10 ~ 1e10 k-points (no body will do this!)
idx_same = (np.diff(k_pos) < 1e-10).nonzero()[0]
# The above algorithm should never create more than two duplicates.
# Hence we can simply remove all idx_same and double the weight for all
# idx_same + 1.
w[idx_same + 1] *= 2
# Delete the duplicated k-points (they are already sorted)
k = np.delete(k_pos, idx_same, axis=0)
w = np.delete(w, idx_same)
else:
# Sort them, because it makes more visual sense
idx = np.argsort(k)
k = k[idx]
w = w[idx]
# Return values
return k, w
